Kalman Filtering and Neural Networks – Simon Haykin – 1st Edition

Preface
Contributors

1 Kalman Filters
1.1 Introduction
1.2 Optimum Estimates
1.3 Kalman Filter
1.4 Divergence Phenomenon: Square-Root Filtering
1.5 Rauch–Tung–Striebel Smoother
1.6 Extended Kalman Filter
1.7 Summary
References

2 Parameter-Based Kalman Filter Training: Theory and Implementation
2.1 Introduction
2.2 Network Architectures
2.3 The EKF Procedure
2.3.1 Global EKF Training
2.3.2 Learning Rate and Scaled Cost Function
2.3.3 Parameter Settings
2.4 Decoupled EKF (DEKF)
2.5 Multistream Training
2.5.1 Some Insight into the Multistream Technique
2.5.2 Advantages and Extensions of Multistream Training
2.6 Computational Considerations
2.6.1 Derivative Calculations
2.6.2 Computationally Efficient Formulations for Multiple-Output Problems
2.6.3 Avoiding Matrix Inversions
2.6.4 Square-Root Filtering
2.7 Other Extensions and Enhancements
2.7.1 EKF Training with Constrained Weights
2.7.2 EKF Training with an Entropic Cost Function
2.7.3 EKF Training with Scalar Errors
2.8 Automotive Applications of EKF Training
2.8.1 Air=Fuel Ratio Control
2.8.2 Idle Speed Control
2.8.3 Sensor-Catalyst Modeling
2.8.4 Engine Misfire Detection
2.8.5 Vehicle Emissions Estimation
2.9 Discussion
2.9.1 Virtues of EKF Training
2.9.2 Limitations of EKF Training
2.9.3 Guidelines for Implementation and Use
References

3 Learning Shape and Motion from Image Sequences
3.1 Introduction
3.2 Neurobiological and Perceptual Foundations of our Model
3.3 Network Description
3.4 Experiment 1
3.5 Experiment 2
3.6 Experiment 3
3.7 Discussion
References

4 Chaotic Dynamics
4.1 Introduction
4.2 Chaotic (Dynamic) Invariants
4.3 Dynamic Reconstruction
4.4 Modeling Numerically Generated Chaotic Time Series
4.4.1 Logistic Map
4.4.2 Ikeda Map
4.4.3 Lorenz Attractor
4.5 Nonlinear Dynamic Modeling of Real-World Time Series
4.5.1 Laser Intensity Pulsations
4.5.2 Sea Clutter Data
4.6 Discussion
References

5 Dual Extended Kalman Filter Methods
5.1 Introduction =
5.2 Dual EKF – Prediction Error
5.2.1 EKF – State Estimation
5.2.2 EKF – Weight Estimation
5.2.3 Dual Estimation
5.3 A Probabilistic Perspective
5.3.1 Joint Estimation Methods
5.3.2 Marginal Estimation Methods
5.3.3 Dual EKF Algorithms
5.3.4 Joint EKF
5.4 Dual EKF Variance Estimation
5.5 Applications
5.5.1 Noisy Time-Series Estimation and Prediction
5.5.2 Economic Forecasting – Index of Industrial Production
5.5.3 Speech Enhancement
5.6 Conclusions
Acknowledgments
Appendix A: Recurrent Derivative of the Kalman Gain
Appendix B: Dual EKF with Colored Measurement Noise
References

6 Learning Nonlinear Dynamical System Using the Expectation-Maximization Algorithm
Sam T. Roweis and Zoubin Ghahramani
6.1 Learning Stochastic Nonlinear Dynamics
6.1.1 State Inference and Model Learning
6.1.2 The Kalman Filter
6.1.3 The EM Algorithm
6.2 Combining EKS and EM
6.2.1 Extended Kalman Smoothing (E-step)
6.2.2 Learning Model Parameters (M-step)
6.2.3 Fitting Radial Basis Functions to Gaussian Clouds
6.2.4 Initialization of Models and Choosing Locations for RBF Kernels
6.3 Results
6.3.1 One- and Two-Dimensional Nonlinear State-Space Models
6.3.2 Weather Data
6.4 Extensions
6.4.1 Learning the Means and Widths of the RBFs
6.4.2 On-Line Learning
6.4.3 Nonstationarity
6.4.4 Using Bayesian Methods for Model Selection and Complexity Control
6.5 Discussion
6.5.1 Identifiability and Expressive Power
6.5.2 Embedded Flows
6.5.3 Stability
6.5.4 Takens’ Theorem and Hidden States
6.5.5 Should Parameters and Hidden States be Treated Differently?
6.6 Conclusions
Acknowledgments
Appendix: Expectations Required to Fit the RBFs
References

7 The Unscented Kalman Filter
Eric A. Wan and Rudolph van der Merwe
7.1 Introduction
7.2 Optimal Recursive Estimation and the EKF
7.3 The Unscented Kalman Filter
7.3.1 State-Estimation Examples
7.3.2 The Unscented Kalman Smoother
7.4 UKF Parameter Estimation
7.4.1 Parameter-Estimation Examples
7.5 UKF Dual Estimation
7.5.1 Dual Estimation Experiments
7.6 The Unscented Particle Filter
7.6.1 The Particle Filter Algorithm
7.6.2 UPF Experiments
7.7 Conclusions

Appendix A: Accuracy of the Unscented Transformation
Appendix B: Efficient Square-Root UKF Implementations
References
Index